Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule

Christian Ringhofer; M. Nedjalkov; H. Kosinas; S. Selberherr

doi:10.1137/S0036139903428914

Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule

Christian Ringhofer, M. Nedjalkov, H. Kosinas, S. Selberherr

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We derive a quantum mechanical correction to the semiclassical Fermi golden rule operator for scattering of electrons in a crystal. This correction takes into account the fact that electron-phonon interaction is not instantaneous in quantum mechanics. The corrective term is derived via an oscillatory, i.e., weak, limit in the Levinson equation for large timescales.

Original language	English (US)
Pages (from-to)	1933-1953
Number of pages	21
Journal	SIAM Journal on Applied Mathematics
Volume	64
Issue number	6
DOIs	https://doi.org/10.1137/S0036139903428914
State	Published - 2004

Keywords

Asymptotic analysis
Boltzmann equation
Fermi's golden rule
Levinson equation
Quantum mechanics
Wigner functions

ASJC Scopus subject areas

Applied Mathematics

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10.1137/S0036139903428914

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title = "Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule",

abstract = "We derive a quantum mechanical correction to the semiclassical Fermi golden rule operator for scattering of electrons in a crystal. This correction takes into account the fact that electron-phonon interaction is not instantaneous in quantum mechanics. The corrective term is derived via an oscillatory, i.e., weak, limit in the Levinson equation for large timescales.",

keywords = "Asymptotic analysis, Boltzmann equation, Fermi's golden rule, Levinson equation, Quantum mechanics, Wigner functions",

author = "Christian Ringhofer and M. Nedjalkov and H. Kosinas and S. Selberherr",

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T1 - Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule

AU - Ringhofer, Christian

AU - Nedjalkov, M.

AU - Kosinas, H.

AU - Selberherr, S.

PY - 2004

Y1 - 2004

N2 - We derive a quantum mechanical correction to the semiclassical Fermi golden rule operator for scattering of electrons in a crystal. This correction takes into account the fact that electron-phonon interaction is not instantaneous in quantum mechanics. The corrective term is derived via an oscillatory, i.e., weak, limit in the Levinson equation for large timescales.

AB - We derive a quantum mechanical correction to the semiclassical Fermi golden rule operator for scattering of electrons in a crystal. This correction takes into account the fact that electron-phonon interaction is not instantaneous in quantum mechanics. The corrective term is derived via an oscillatory, i.e., weak, limit in the Levinson equation for large timescales.

KW - Asymptotic analysis

KW - Boltzmann equation

KW - Fermi's golden rule

KW - Levinson equation

KW - Quantum mechanics

KW - Wigner functions

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JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 6

ER -

Semiclassical approximation of electron-phonon scattering beyond Fermi's golden rule

Abstract

Keywords

ASJC Scopus subject areas

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